It is well known that the reaction of naphthalene with propylene gives 2,6-diisopropylnaphthalene which is an important raw material for the production of 2,6-naphthalenedicarboxylic acid which in turn is useful for the fabrication of polyesters. Known processes are, however, not fully satisfactory from industrial point of view, since the reaction also yields a significant amount of other structural isomers, monoisopropylnaphthalenes and triisopropylnaphthalenes. It is also known to subject the reaction mixture obtained by the above isopropylation reaction to transalkylation conditions to convert monoisopropylnaphthalenes to diisopropylnaphthalenes. While such transalkylation can improve the yield of di-substituted products, the yield of the desired 2,6-substituted product is still unsatisfactory. Further, it is very difficult to isomerize diisopropylnaphthalenes to 2,6-diisopropylnaphthalene. Thus, there is a great demand for a process which can give 2,6-diisopropylnaphthalene with a high yield.